Subgroups — C₅×#19279 #11941999

Order 1280.

712 conjugacy classes of subgroups.

The subgroup lattice has 498 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#3167	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅×#3077	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×#3036	C₂	1	1	yes	maximal, characteristic
4	C₂×C₅×#436	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#1699	C₂	1	2	yes	maximal, complemented
6	C₅×#1697	C₂	1	2	yes	maximal, complemented
7	C₅×#1691	C₂	1	2	yes	maximal, complemented
8	C₅×#1685	C₂	1	2	yes	maximal, complemented
9	C₅×#1567	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅×#1550	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅×#1547	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₅×AGL(1,ℤ/8)	—	2	1	no	—
13	C₂²×C₅×M₁₆	—	2	1	no	—
14	C₅×#533	C₂²	1	1	yes	characteristic
15	C₅×#532	C₂²	1	1	yes	characteristic
16	C₂×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
17	C₅×#498	C₂²	1	1	yes	characteristic, complemented
18	C₅×#492	C₂²	1	1	yes	characteristic, complemented
19	C₅×#487	C₂²	1	1	yes	characteristic, complemented
20	C₅×#486	C₂²	1	1	yes	characteristic, complemented
21	C₅×#478	—	2	2	no	—
22	C₅×#476	C₂²	1	2	yes	—
23	C₅×#474	C₂²	1	2	yes	—
24	C₅×#465	—	2	1	no	—
25	C₅×#465	—	2	1	no	—
26	C₅×#463	—	2	2	no	—
27	C₅×#461	C₂²	1	2	yes	—
28	C₅×#459	C₂²	1	2	yes	—
29	C₄×C₅×SD₁₆	—	2	1	no	—
30	C₄×C₅×SD₁₆	—	2	1	no	—
31	C₅×#436	—	2	1	no	—
32	C₅×#436	—	2	1	no	—
33	C₅×#436	C₂²	1	2	yes	—
34	C₅×#436	C₂²	1	2	yes	—
35	C₅×#428	—	2	1	no	—
36	C₅×#423	C₂²	1	1	yes	characteristic
37	C₅×#423	C₂²	1	1	yes	characteristic
38	C₂×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic
39	C₅×#418	—	2	1	no	—
40	C₅×#417	—	2	1	no	—
41	C₂×C₅×C₂²⋊C₈	—	2	1	no	—
42	C₂×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
43	C₅×#335	C₂²	1	2	yes	complemented
44	C₅×#335	C₂²	1	2	yes	complemented
45	C₅×#333	C₂²	1	2	yes	complemented
46	C₅×#332	C₂²	1	2	yes	complemented
47	C₅×#332	C₂²	1	2	yes	complemented
48	C₅×#331	C₂²	1	2	yes	complemented
49	#19279	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
50	C₂×C₅×#41	—	2	1	no	—
51	C₂²×C₅×D₄	D₄	1	1	yes	characteristic
52	C₂³×C₄×C₅	—	2	1	no	—
53	C₅×AGL(1,ℤ/8)	—	4	4	no	—
54	C₂×C₅×SD₁₆	—	2	2	no	—
55	C₂×C₅×SD₁₆	—	2	1	no	—
56	C₂×C₅×SD₁₆	—	2	1	no	—
57	C₂×C₅×D₈	—	2	2	no	—
58	C₂×C₅×M₁₆	—	2	1	no	—
59	C₂×C₅×M₁₆	—	2	1	no	—
60	C₂×C₅×M₁₆	—	2	2	no	—
61	C₂×C₅×M₁₆	—	2	2	no	—
62	C₂×C₅×M₁₆	—	4	4	no	—
63	C₂²×C₅×C₈	—	2	1	no	—
64	C₂²×C₅×C₈	D₄	1	1	yes	characteristic
65	C₂²×C₅×C₈	D₄	1	1	yes	characteristic
66	C₅×C₄⋊Q₈	C₂³	1	1	yes	characteristic
67	C₅×C₄⋊Q₈	C₂³	1	1	yes	characteristic
68	C₅×C₄⋊Q₈	C₂³	1	1	yes	characteristic
69	C₅×#127	C₂³	1	1	yes	characteristic
70	C₅×#125	—	2	1	no	—
71	C₅×#124	—	2	1	no	—
72	C₅×C₂²⋊Q₈	—	2	1	no	—
73	C₅×C₂²⋊Q₈	—	2	1	no	—
74	C₅×#121	—	2	1	no	—
75	C₅×#121	—	2	1	no	—
76	C₄×C₅×Q₈	—	2	1	no	—
77	C₄×C₅×Q₈	—	2	1	no	—
78	C₄×C₅×D₄	—	2	1	no	—
79	C₄×C₅×D₄	—	2	1	no	—
80	C₄×C₅×D₄	—	2	1	no	—
81	C₄×C₅×D₄	—	2	1	no	—
82	C₄×C₅×D₄	D₄	1	2	yes	—
83	C₄×C₅×D₄	C₂³	1	2	yes	—
84	C₅×#117	—	2	1	no	—
85	C₂×C₅×C₄⋊C₄	D₄	1	1	yes	characteristic
86	C₂×C₅×C₂²⋊C₄	—	2	1	no	—
87	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
88	C₅×#107	—	2	2	no	—
89	C₅×#106	—	2	1	no	—
90	C₅×#106	—	2	1	no	—
91	C₅×#106	—	2	2	no	—
92	C₅×C₄⋊C₈	—	2	1	no	—
93	C₅×C₄⋊C₈	—	2	1	no	—
94	C₅×C₄⋊C₈	—	2	1	no	—
95	C₅×C₄⋊C₈	C₂³	1	2	yes	—
96	C₅×C₄⋊C₈	C₂³	1	2	yes	—
97	C₅×C₄⋊C₈	C₂³	1	2	yes	—
98	C₅×#103	—	2	1	no	—
99	C₅×#103	—	2	1	no	—
100	C₅×#103	—	2	2	no	—
101	C₅×#102	—	2	2	no	—
102	C₅×#102	—	2	2	no	—
103	C₅×#102	—	2	1	no	—
104	C₅×#102	—	2	1	no	—
105	C₅×#102	—	2	2	no	—
106	C₅×C₂²⋊C₈	—	2	2	no	—
107	C₅×C₂²⋊C₈	—	2	2	no	—
108	C₄×C₅×C₈	D₄	1	1	yes	characteristic
109	C₄×C₅×C₈	D₄	1	1	yes	characteristic
110	C₄×C₅×C₈	C₂³	1	1	yes	characteristic
111	C₄×C₅×C₈	C₂³	1	1	yes	characteristic
112	#3167	C₂×C₅	1	1	yes	characteristic, complemented
113	#3077	C₂×C₅	1	1	yes	characteristic, complemented
114	#3036	C₂×C₅	1	1	yes	characteristic
115	C₂×#436	C₂×C₅	1	1	yes	characteristic, complemented
116	#1699	C₂×C₅	1	2	yes	complemented
117	#1697	C₂×C₅	1	2	yes	complemented
118	#1691	C₂×C₅	1	2	yes	complemented
119	#1685	C₂×C₅	1	2	yes	complemented
120	#1567	C₂×C₅	1	1	yes	characteristic, complemented
121	#1550	C₂×C₅	1	1	yes	characteristic, complemented
122	#1547	C₂×C₅	1	1	yes	characteristic, complemented
123	C₂⁴×C₅	—	2	1	no	—
124	C₅×#41	—	4	2	no	—
125	C₅×#41	—	4	2	no	—
126	C₂×C₅×Q₈	—	2	1	no	—
127	C₂×C₅×Q₈	—	2	1	no	—
128	C₂×C₅×Q₈	—	2	1	no	—
129	C₂×C₅×D₄	—	2	1	no	—
130	C₂×C₅×D₄	—	2	2	no	—
131	C₂×C₅×D₄	—	2	2	no	—
132	C₂×C₅×D₄	—	2	1	no	—
133	C₂×C₅×D₄	—	2	1	no	—
134	C₂×C₅×D₄	—	2	1	no	—
135	C₂×C₅×D₄	—	4	1	no	—
136	C₂×C₅×D₄	C₂×D₄	1	2	yes	—
137	C₂²×C₄×C₅	—	2	1	no	—
138	C₂²×C₄×C₅	—	2	2	no	—
139	C₂²×C₄×C₅	—	2	2	no	—
140	C₂²×C₄×C₅	—	4	2	no	—
141	C₂²×C₄×C₅	—	4	2	no	—
142	C₂²×C₄×C₅	—	4	1	no	—
143	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
144	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
145	C₂²×C₄×C₅	#41	1	1	yes	characteristic
146	C₅×SD₁₆	—	4	2	no	—
147	C₅×SD₁₆	—	4	4	no	—
148	C₅×SD₁₆	—	4	2	no	—
149	C₅×D₈	—	4	4	no	—
150	C₅×M₁₆	—	4	4	no	—
151	C₅×M₁₆	—	4	2	no	—
152	C₅×M₁₆	—	4	2	no	—
153	C₅×M₁₆	—	4	4	no	—
154	C₂×C₅×C₈	—	2	2	no	—
155	C₂×C₅×C₈	—	2	2	no	—
156	C₂×C₅×C₈	—	2	2	no	—
157	C₂×C₅×C₈	—	2	2	no	—
158	C₂×C₅×C₈	—	4	1	no	—
159	C₂×C₅×C₈	—	4	2	no	—
160	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
161	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
162	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
163	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
164	C₅×C₄⋊C₄	—	2	1	no	—
165	C₅×C₄⋊C₄	—	2	1	no	—
166	C₅×C₄⋊C₄	—	2	1	no	—
167	C₅×C₄⋊C₄	—	2	1	no	—
168	C₅×C₄⋊C₄	—	2	1	no	—
169	C₅×C₄⋊C₄	—	2	1	no	—
170	C₅×C₄⋊C₄	—	2	1	no	—
171	C₅×C₄⋊C₄	—	4	1	no	—
172	C₅×C₄⋊C₄	—	4	1	no	—
173	C₅×C₄⋊C₄	C₂×D₄	1	2	yes	—
174	C₅×C₂²⋊C₄	—	2	2	no	—
175	C₅×C₂²⋊C₄	—	2	2	no	—
176	C₅×C₂²⋊C₄	—	4	1	no	—
177	C₅×C₂²⋊C₄	—	4	1	no	—
178	C₅×C₂²⋊C₄	—	4	1	no	—
179	C₄²×C₅	—	4	1	no	—
180	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
181	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
182	C₄²×C₅	#41	1	1	yes	characteristic
183	C₄²×C₅	C₂⁴	1	1	yes	characteristic
184	C₂×AGL(1,ℤ/8)	—	2	1	no	—
185	C₂²×M₁₆	—	2	1	no	—
186	#533	C₂²×C₅	1	1	yes	characteristic
187	#532	C₂²×C₅	1	1	yes	characteristic
188	C₂×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
189	#498	C₂²×C₅	1	1	yes	characteristic, complemented
190	#492	C₂²×C₅	1	1	yes	characteristic, complemented
191	#487	C₂²×C₅	1	1	yes	characteristic, complemented
192	#486	C₂²×C₅	1	1	yes	characteristic, complemented
193	#478	—	2	2	no	—
194	#476	C₂²×C₅	1	2	yes	—
195	#474	C₂²×C₅	1	2	yes	—
196	#465	—	2	1	no	—
197	#465	—	2	1	no	—
198	#463	—	2	2	no	—
199	#461	C₂²×C₅	1	2	yes	—
200	#459	C₂²×C₅	1	2	yes	—
201	C₄×SD₁₆	—	2	1	no	—
202	C₄×SD₁₆	—	2	1	no	—
203	#436	—	2	1	no	—
204	#436	—	2	1	no	—
205	#436	C₂²×C₅	1	2	yes	—
206	#436	C₂²×C₅	1	2	yes	—
207	#428	—	2	1	no	—
208	#423	C₂²×C₅	1	1	yes	characteristic
209	#423	C₂²×C₅	1	1	yes	characteristic
210	C₂×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
211	#418	—	2	1	no	—
212	#417	—	2	1	no	—
213	C₂×C₂²⋊C₈	—	2	1	no	—
214	C₂×C₄×C₈	C₂²×C₅	1	1	yes	characteristic
215	#335	C₂²×C₅	1	2	yes	complemented
216	#335	C₂²×C₅	1	2	yes	complemented
217	#333	C₂²×C₅	1	2	yes	complemented
218	#332	C₂²×C₅	1	2	yes	complemented
219	#332	C₂²×C₅	1	2	yes	complemented
220	#331	C₂²×C₅	1	2	yes	complemented
221	C₂³×C₅	—	2	2	no	—
222	C₂³×C₅	—	4	2	no	—
223	C₂³×C₅	—	4	2	no	—
224	C₂³×C₅	—	4	2	no	—
225	C₂³×C₅	—	4	1	no	—
226	C₂³×C₅	#121	1	1	yes	characteristic
227	C₅×Q₈	—	4	1	no	—
228	C₅×Q₈	—	4	1	no	—
229	C₅×Q₈	—	4	1	no	—
230	C₅×Q₈	—	4	1	no	—
231	C₅×Q₈	—	8	1	no	—
232	C₅×D₄	—	2	2	no	—
233	C₅×D₄	—	2	2	no	—
234	C₅×D₄	—	4	1	no	—
235	C₅×D₄	—	4	1	no	—
236	C₅×D₄	—	4	1	no	—
237	C₅×D₄	—	4	1	no	—
238	C₅×D₄	—	4	2	no	—
239	C₅×D₄	—	8	1	no	—
240	C₅×D₄	—	8	2	no	—
241	C₂×C₄×C₅	—	2	1	no	—
242	C₂×C₄×C₅	—	2	1	no	—
243	C₂×C₄×C₅	—	2	2	no	—
244	C₂×C₄×C₅	—	4	1	no	—
245	C₂×C₄×C₅	—	4	4	no	—
246	C₂×C₄×C₅	—	4	2	no	—
247	C₂×C₄×C₅	—	4	2	no	—
248	C₂×C₄×C₅	—	4	2	no	—
249	C₂×C₄×C₅	—	4	1	no	—
250	C₂×C₄×C₅	—	4	1	no	—
251	C₂×C₄×C₅	—	4	1	no	—
252	C₂×C₄×C₅	—	8	2	no	—
253	C₂×C₄×C₅	#121	1	1	yes	characteristic
254	C₂×C₄×C₅	#121	1	1	yes	characteristic
255	C₂×C₄×C₅	#121	1	1	yes	characteristic
256	C₂×C₄×C₅	AGL(1,ℤ/8)	1	2	yes	—
257	C₂×C₄×C₅	#137	1	2	yes	—
258	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
259	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
260	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
261	C₅×C₈	—	2	1	no	—
262	C₅×C₈	—	2	1	no	—
263	C₅×C₈	—	2	1	no	—
264	C₅×C₈	—	4	2	no	—
265	C₅×C₈	—	4	2	no	—
266	C₅×C₈	—	4	2	no	—
267	C₅×C₈	AGL(1,ℤ/8)	1	2	yes	complemented
268	C₂×#41	—	2	1	no	—
269	C₂²×D₄	C₅×D₄	1	1	yes	characteristic
270	C₂³×C₄	—	2	1	no	—
271	AGL(1,ℤ/8)	—	4	4	no	—
272	C₂×SD₁₆	—	2	2	no	—
273	C₂×SD₁₆	—	2	1	no	—
274	C₂×SD₁₆	—	2	1	no	—
275	C₂×D₈	—	2	2	no	—
276	C₂×M₁₆	—	2	1	no	—
277	C₂×M₁₆	—	2	1	no	—
278	C₂×M₁₆	—	2	2	no	—
279	C₂×M₁₆	—	2	2	no	—
280	C₂×M₁₆	—	4	4	no	—
281	C₂²×C₈	—	2	1	no	—
282	C₂²×C₈	C₅×D₄	1	1	yes	characteristic
283	C₂²×C₈	C₅×D₄	1	1	yes	characteristic
284	C₄⋊Q₈	C₂³×C₅	1	1	yes	characteristic
285	C₄⋊Q₈	C₂³×C₅	1	1	yes	characteristic
286	C₄⋊Q₈	C₂³×C₅	1	1	yes	characteristic
287	#127	C₂³×C₅	1	1	yes	characteristic
288	#125	—	2	1	no	—
289	#124	—	2	1	no	—
290	C₂²⋊Q₈	—	2	1	no	—
291	C₂²⋊Q₈	—	2	1	no	—
292	#121	—	2	1	no	—
293	#121	—	2	1	no	—
294	C₄×Q₈	—	2	1	no	—
295	C₄×Q₈	—	2	1	no	—
296	C₄×D₄	—	2	1	no	—
297	C₄×D₄	—	2	1	no	—
298	C₄×D₄	—	2	1	no	—
299	C₄×D₄	—	2	1	no	—
300	C₄×D₄	C₅×D₄	1	2	yes	—
301	C₄×D₄	C₂³×C₅	1	2	yes	—
302	#117	—	2	1	no	—
303	C₂×C₄⋊C₄	C₅×D₄	1	1	yes	characteristic
304	C₂×C₂²⋊C₄	—	2	1	no	—
305	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
306	#107	—	2	2	no	—
307	#106	—	2	1	no	—
308	#106	—	2	1	no	—
309	#106	—	2	2	no	—
310	C₄⋊C₈	—	2	1	no	—
311	C₄⋊C₈	—	2	1	no	—
312	C₄⋊C₈	—	2	1	no	—
313	C₄⋊C₈	C₂³×C₅	1	2	yes	—
314	C₄⋊C₈	C₂³×C₅	1	2	yes	—
315	C₄⋊C₈	C₂³×C₅	1	2	yes	—
316	#103	—	2	1	no	—
317	#103	—	2	1	no	—
318	#103	—	2	2	no	—
319	#102	—	2	2	no	—
320	#102	—	2	2	no	—
321	#102	—	2	1	no	—
322	#102	—	2	1	no	—
323	#102	—	2	2	no	—
324	C₂²⋊C₈	—	2	2	no	—
325	C₂²⋊C₈	—	2	2	no	—
326	C₄×C₈	C₅×D₄	1	1	yes	characteristic
327	C₄×C₈	C₅×D₄	1	1	yes	characteristic
328	C₄×C₈	C₂³×C₅	1	1	yes	characteristic
329	C₄×C₈	C₂³×C₅	1	1	yes	characteristic
330	C₂²×C₅	—	2	1	no	—
331	C₂²×C₅	—	2	1	no	—
332	C₂²×C₅	—	4	2	no	—
333	C₂²×C₅	—	4	2	no	—
334	C₂²×C₅	—	4	2	no	—
335	C₂²×C₅	—	8	4	no	—
336	C₂²×C₅	—	8	1	no	—
337	C₂²×C₅	—	8	1	no	—
338	C₂²×C₅	—	8	1	no	—
339	C₂²×C₅	#468	1	2	yes	—
340	C₂²×C₅	C₂×#121	1	1	yes	characteristic
341	C₄×C₅	—	2	1	no	—
342	C₄×C₅	—	2	1	no	—
343	C₄×C₅	—	2	1	no	—
344	C₄×C₅	—	4	2	no	—
345	C₄×C₅	—	8	1	no	—
346	C₄×C₅	—	8	1	no	—
347	C₄×C₅	—	8	1	no	—
348	C₄×C₅	#468	1	2	yes	—
349	C₄×C₅	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
350	C₄×C₅	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
351	C₄×C₅	C₂×#137	1	1	yes	characteristic
352	C₄×C₅	#575	1	1	yes	characteristic
353	C₂⁴	—	2	1	no	—
354	#41	—	4	2	no	—
355	#41	—	4	2	no	—
356	C₂×Q₈	—	2	1	no	—
357	C₂×Q₈	—	2	1	no	—
358	C₂×Q₈	—	2	1	no	—
359	C₂×D₄	—	2	1	no	—
360	C₂×D₄	—	2	2	no	—
361	C₂×D₄	—	2	2	no	—
362	C₂×D₄	—	2	1	no	—
363	C₂×D₄	—	2	1	no	—
364	C₂×D₄	—	2	1	no	—
365	C₂×D₄	—	4	1	no	—
366	C₂×D₄	C₂×C₅×D₄	1	2	yes	—
367	C₂²×C₄	—	2	1	no	—
368	C₂²×C₄	—	2	2	no	—
369	C₂²×C₄	—	2	2	no	—
370	C₂²×C₄	—	4	2	no	—
371	C₂²×C₄	—	4	2	no	—
372	C₂²×C₄	—	4	1	no	—
373	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
374	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
375	C₂²×C₄	C₅×#41	1	1	yes	characteristic
376	SD₁₆	—	4	2	no	—
377	SD₁₆	—	4	4	no	—
378	SD₁₆	—	4	2	no	—
379	D₈	—	4	4	no	—
380	M₁₆	—	4	4	no	—
381	M₁₆	—	4	2	no	—
382	M₁₆	—	4	2	no	—
383	M₁₆	—	4	4	no	—
384	C₂×C₈	—	2	2	no	—
385	C₂×C₈	—	2	2	no	—
386	C₂×C₈	—	2	2	no	—
387	C₂×C₈	—	2	2	no	—
388	C₂×C₈	—	4	1	no	—
389	C₂×C₈	—	4	2	no	—
390	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
391	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
392	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
393	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
394	C₄⋊C₄	—	2	1	no	—
395	C₄⋊C₄	—	2	1	no	—
396	C₄⋊C₄	—	2	1	no	—
397	C₄⋊C₄	—	2	1	no	—
398	C₄⋊C₄	—	2	1	no	—
399	C₄⋊C₄	—	2	1	no	—
400	C₄⋊C₄	—	2	1	no	—
401	C₄⋊C₄	—	4	1	no	—
402	C₄⋊C₄	—	4	1	no	—
403	C₄⋊C₄	C₂×C₅×D₄	1	2	yes	—
404	C₂²⋊C₄	—	2	2	no	—
405	C₂²⋊C₄	—	2	2	no	—
406	C₂²⋊C₄	—	4	1	no	—
407	C₂²⋊C₄	—	4	1	no	—
408	C₂²⋊C₄	—	4	1	no	—
409	C₄²	—	4	1	no	—
410	C₄²	C₂×C₅×D₄	1	1	yes	characteristic
411	C₄²	C₂×C₅×D₄	1	1	yes	characteristic
412	C₄²	C₅×#41	1	1	yes	characteristic
413	C₄²	C₂⁴×C₅	1	1	yes	characteristic
414	C₂×C₅	—	2	2	no	—
415	C₂×C₅	—	8	2	no	—
416	C₂×C₅	—	16	1	no	—
417	C₂×C₅	#3036	1	1	yes	characteristic
418	C₂×C₅	C₂×#468	1	1	yes	characteristic
419	C₂×C₅	#3067	1	1	yes	characteristic
420	C₂³	—	2	2	no	—
421	C₂³	—	4	2	no	—
422	C₂³	—	4	2	no	—
423	C₂³	—	4	2	no	—
424	C₂³	—	4	1	no	—
425	C₂³	C₅×#121	1	1	yes	characteristic
426	Q₈	—	4	1	no	—
427	Q₈	—	4	1	no	—
428	Q₈	—	4	1	no	—
429	Q₈	—	4	1	no	—
430	Q₈	—	8	1	no	—
431	D₄	—	2	2	no	—
432	D₄	—	2	2	no	—
433	D₄	—	4	2	no	—
434	D₄	—	4	1	no	—
435	D₄	—	4	1	no	—
436	D₄	—	4	1	no	—
437	D₄	—	4	1	no	—
438	D₄	—	8	1	no	—
439	D₄	—	8	2	no	—
440	C₂×C₄	—	2	1	no	—
441	C₂×C₄	—	2	1	no	—
442	C₂×C₄	—	2	2	no	—
443	C₂×C₄	—	4	1	no	—
444	C₂×C₄	—	4	4	no	—
445	C₂×C₄	—	4	2	no	—
446	C₂×C₄	—	4	2	no	—
447	C₂×C₄	—	4	2	no	—
448	C₂×C₄	—	4	1	no	—
449	C₂×C₄	—	4	1	no	—
450	C₂×C₄	—	4	1	no	—
451	C₂×C₄	—	8	2	no	—
452	C₂×C₄	C₅×#121	1	1	yes	characteristic
453	C₂×C₄	C₅×#121	1	1	yes	characteristic
454	C₂×C₄	C₅×#121	1	1	yes	characteristic
455	C₂×C₄	C₅×AGL(1,ℤ/8)	1	2	yes	—
456	C₂×C₄	C₅×#137	1	2	yes	—
457	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
458	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
459	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
460	C₈	—	2	1	no	—
461	C₈	—	2	1	no	—
462	C₈	—	2	1	no	—
463	C₈	—	4	2	no	—
464	C₈	—	4	2	no	—
465	C₈	—	4	2	no	—
466	C₈	C₅×AGL(1,ℤ/8)	1	2	yes	complemented
467	C₅	#19279	1	1	yes	characteristic, direct product factor, Sylow
468	C₂²	—	2	1	no	—
469	C₂²	—	2	1	no	—
470	C₂²	—	4	2	no	—
471	C₂²	—	4	2	no	—
472	C₂²	—	4	2	no	—
473	C₂²	—	8	4	no	—
474	C₂²	—	8	1	no	—
475	C₂²	—	8	1	no	—
476	C₂²	—	8	1	no	—
477	C₂²	C₅×#468	1	2	yes	—
478	C₂²	C₂×C₅×#121	1	1	yes	characteristic
479	C₄	—	2	1	no	—
480	C₄	—	2	1	no	—
481	C₄	—	2	1	no	—
482	C₄	—	4	2	no	—
483	C₄	—	8	1	no	—
484	C₄	—	8	1	no	—
485	C₄	—	8	1	no	—
486	C₄	C₅×#468	1	2	yes	—
487	C₄	C₂×C₅×AGL(1,ℤ/8)	1	1	yes	characteristic
488	C₄	C₂×C₅×AGL(1,ℤ/8)	1	1	yes	characteristic
489	C₄	C₂×C₅×#137	1	1	yes	characteristic
490	C₄	C₅×#575	1	1	yes	characteristic
491	C₂	—	2	2	no	—
492	C₂	—	8	2	no	—
493	C₂	—	16	1	no	—
494	C₂	C₅×#3036	1	1	yes	characteristic
495	C₂	C₂×C₅×#468	1	1	yes	characteristic
496	C₂	C₅×#3067	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₅	C₂×#121
commutator, Frattini, cosocle	C₄²	C₂⁴×C₅
prime radical	C₅×#3036	C₂
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₅ ◁ C₂×C₄²×C₅ ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
1. C₅×#3167	C₂	semidirect
2. C₅×#3077	C₂	semidirect
4. C₂×C₅×#436	C₂	semidirect
5. C₅×#1699	C₂	semidirect
6. C₅×#1697	C₂	semidirect
7. C₅×#1691	C₂	semidirect
8. C₅×#1685	C₂	semidirect
9. C₅×#1567	C₂	semidirect
10. C₅×#1550	C₂	semidirect
11. C₅×#1547	C₂	semidirect
17. C₅×#498	C₂²	semidirect
18. C₅×#492	C₂²	semidirect
19. C₅×#487	C₂²	semidirect
20. C₅×#486	C₂²	semidirect
43. C₅×#335	C₂²	semidirect
44. C₅×#335	C₂²	semidirect
45. C₅×#333	C₂²	semidirect
46. C₅×#332	C₂²	semidirect
47. C₅×#332	C₂²	semidirect
48. C₅×#331	C₂²	semidirect
49. #19279	C₅	direct (N × H)
112. #3167	C₂×C₅	semidirect
113. #3077	C₂×C₅	semidirect
115. C₂×#436	C₂×C₅	semidirect
116. #1699	C₂×C₅	semidirect
117. #1697	C₂×C₅	semidirect
118. #1691	C₂×C₅	semidirect
119. #1685	C₂×C₅	semidirect
120. #1567	C₂×C₅	semidirect
121. #1550	C₂×C₅	semidirect
122. #1547	C₂×C₅	semidirect
189. #498	C₂²×C₅	semidirect
190. #492	C₂²×C₅	semidirect
191. #487	C₂²×C₅	semidirect
192. #486	C₂²×C₅	semidirect
215. #335	C₂²×C₅	semidirect
216. #335	C₂²×C₅	semidirect
217. #333	C₂²×C₅	semidirect
218. #332	C₂²×C₅	semidirect
219. #332	C₂²×C₅	semidirect
220. #331	C₂²×C₅	semidirect
267. C₅×C₈	AGL(1,ℤ/8)	semidirect
466. C₈	C₅×AGL(1,ℤ/8)	semidirect
467. C₅	#19279	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₅×#3167	2
C₅×#3077	2
C₅×#3036	2
C₂×C₅×#436	2
C₅×#1699	2
C₅×#1697	2
C₅×#1691	2
C₅×#1685	2
C₅×#1567	2
C₅×#1550	2
C₅×#1547	2
#19279	5

Subgroups — C5×#19279 #11941999

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#19279 #11941999